수치편미분방정식

연세대학교
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페이스북 트위터 카카오톡 네이버밴드 링크복사

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자연과학 >수학ㆍ물리ㆍ천문ㆍ지리 >수학
강의학기

2011년 1학기

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14,844

This course focuses on the fundamentals of modern numerical techniques for a wide range of linear and nonlinear elliptic, parabolic, and hyperbolic partial differential equations and integral equations central to a wide variety of applications in science, engineering, and other fields. Topics includes : Mathematical formulations; Finite difference method, Finite volume method, Collocation method, Finite element method

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Introduction of this course 1-1

차시별 강의

1.	Introduction of this course 1-1	1. Introduction of this course 2. Preliminaries
2.	Introduction of this course 1-2
3.	Introduction of this course 2	1. Introduction of this course 2. Preliminaries
4.	Steady state and Boundary value problems 1	1. Heat Equation 2. Locla Trucation error, Global error 3. Dirichlet-Neumann Boundary condition
5.	Steady state and Boundary value problems 2	1. Dirichlet-Neumann boundary condition 2. Neumann boundary conditon 3. 2D steady state heat equation
6.	Steady state and Boundary value problem	1. 2D steady state heat equation 2. Singular perturbation and boundary layer
7.	The Initial Value Problem for Ordinary Differential Equations 1	1. Linear Ordinary Differential Equation 2. Lipschitz continuity
8.	The Initial Value Problem for Ordinary Differential Equations	One-step method for ODE
9.	The Initial Value Problem for Ordinary Differential Equations	Multistep method for ODE
10.	Zero-Stability and Convergence for Initial value Problem	Stability of one-step method
11.	Absolute Stability for Ordinary Differential Equations	Absolute Stability of one-step and multistep methods, Stability Regions
12.	Diffusion Equations and Parabolic Problems	Discretization of Diffusion Equations
13.	Diffusion Equations and Parabolic Problems	Matrix form of Crank-Nicolson, LTE, Stability
14.	Diffusion Equations and Parabolic Problems	Stability of Crank-Nicolson and Forward Euler
15.	Diffusion Equations and Parabolic Problems	Stiffness of heat equations, Convergence
16.	Diffusion Equations and Parabolic Problems	Lax Equivalence Theorem, Von-Neumann Analysis
17.	Diffusion Equations and Parabolic Problems	Von-Neumann Analysis, Multidimensional Problems
18.	Advection Equations and Hyperbolic equations	Method of Lines Discretiztion(MOL)
19.	Advection Equations and Hyperbolic equations	Method of Lines Discretiztion, Von-Neumann Analysis for MOL
20.	Advection Equations and Hyperbolic equations	Von-Neumann Analysis, CFL condition
21.	Finite Volume Method	Conservation Law, General Formulation
22.	Finite Volume Method	Conservation Law, CFLcondition, Numerical Fluxes
23.	Finite Volume Method	Numerical Fluxes
24.	Finite Volume Method	Limiters
25.	Finite Volume Method	Limiters, TVD
26.	Finite Volume Method	FVM in n-dimensional space
27.	Finite Volume Method	FVM in n-dimensional space
28.	Finite Element Method	Sobolev Spaces
29.	Finite Element Method	Sobolev Spaces
30.	Finite Element Method	Sobolev Spaces
31.	Finite Element Method	FEM - Implementation
32.	Finite Element Method	FEM - Implementation
33.	Finite Element Method	FEM for 2D Poissong Equation, ProgrammingWeak solutions
34.	Finite Element Method	Existence and Uniqueness of weak solutions
35.	Finite Element Method	Dirichlet Problem, Neumann Problem
36.	Finite Element Method	Minimization Problem, Discrete Problem